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Hudson wants to build a rectangular enclosure for his animals. One side of the pen will be against the barn, so he needs no fence on that side. The other three sides will be enclosed with wire fencing. If Hudson has 450 feet of fencing, you can find the dimensions that maximize the area of the enclosure.

a) Let `w` be the width of the enclosure (perpendicular to the barn) and let `l` be the length of the enclosure (parallel to the barn). Write an function for the area `A` of the enclosure in terms of `w`. (HINT first write two equations with `w` and `l` and `A`. Solve for `l` in one equation and substitute for `l` in the other).

`A(w) =`

b) What width `w` would maximize the area?

`w` = ft

c) What is the maximum area?

`A` = square feet

a) Let `w` be the width of the enclosure (perpendicular to the barn) and let `l` be the length of the enclosure (parallel to the barn). Write an function for the area `A` of the enclosure in terms of `w`. (HINT first write two equations with `w` and `l` and `A`. Solve for `l` in one equation and substitute for `l` in the other).

`A(w) =`

b) What width `w` would maximize the area?

`w` = ft

c) What is the maximum area?

`A` = square feet

Box 1: Enter your answer as an expression. Example: 3x^2+1, x/5, (a+b)/c

Be sure your variables match those in the question

`w*(450 - 2*w)`

Box 2: Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)

Enter DNE for Does Not Exist, oo for Infinity

112.5

Box 3: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172

Enter DNE for Does Not Exist, oo for Infinity

25312.5